Order-p: an Algorithm to Order Network Partitionings

A network partitioning is said to occur when failures fragment the network into two or more sub-networks. This causes the performance of the network to degrade and many techniques have been proposed to combat this degradation. The number of possible partitionings in a fully connected network of n nodes is greater than 2 n , for large n. Thus, the analysis of partitioning-resilient algorithms is extremely diicult due to the diiculty encountered in computing the probabilities of occurrence of various partitionings. In this paper, we propose an algorithm that orders network partitionings in decreasing order of probability. This algorithm is similar to the Most Probable State Enumeration (MPSE) algorithm proposed by Li and Silvester. By looking at only the most probable partitionings, a good estimate of the performance of the network may be obtained. This approach also gives bounds on the network performance.